Logical Reasoning

Visual Reasoning

Medium

Which of the following numbers, when placed at the sign of interrogation (?) will complete the given pattern?

130

150

180

110

✅ Correct Option: 1

The big triangle is divided into 6 smaller triangular sectors. Let's look at the mathematical pattern behind the numbers in each sector, starting from the top-left and moving counter-clockwise:

Top-Left Sector: $2$

$2 = 1^3 + 1$

Middle-Left Sector: $6$

$6 = 2^3 - 2$

Bottom-Left Sector: $30$

$30 = 3^3 + 3$

Bottom-Right Sector: $60$

$60 = 4^3 - 4$

Middle-Right Sector (?)

Following the alternating $(+ / -)$ sequence of $n^3 \pm n$ :

$\text{?} = 5^3 + 5 = 125 + 5 = \mathbf{130}$

Top-Right Sector: $210$

Continuing the pattern to verify:

$210 = 6^3 - 6 = 216 - 6 = 210$

The mathematical logic perfectly fits every sector. Thus, the missing number is 130.

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2023: 19 June Shift 1

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Which of the following numbers, when placed at the sign of interrogation (?) will complete the given pattern?

Solution

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